<?php

/**
 * @package JAMA
 *
 *    For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
 *    unit lower triangular matrix L, an n-by-n upper triangular matrix U,
 *    and a permutation vector piv of length m so that A(piv,:) = L*U.
 *    If m < n, then L is m-by-m and U is m-by-n.
 *
 *    The LU decompostion with pivoting always exists, even if the matrix is
 *    singular, so the constructor will never fail. The primary use of the
 *    LU decomposition is in the solution of square systems of simultaneous
 *    linear equations. This will fail if isNonsingular() returns false.
 *
 * @author Paul Meagher
 * @author Bartosz Matosiuk
 * @author Michael Bommarito
 * @version 1.1
 * @license PHP v3.0
 */
class PHPExcel_Shared_JAMA_LUDecomposition
{
	const MATRIX_SINGULAR_EXCEPTION = "Can only perform operation on singular matrix.";
	const MATRIX_SQUARE_EXCEPTION = "Mismatched Row dimension";
	
	/**
	 *    Decomposition storage
	 * @var array
	 */
	private $LU = array();
	
	/**
	 *    Row dimension.
	 * @var int
	 */
	private $m;
	
	/**
	 *    Column dimension.
	 * @var int
	 */
	private $n;
	
	/**
	 *    Pivot sign.
	 * @var int
	 */
	private $pivsign;
	
	/**
	 *    Internal storage of pivot vector.
	 * @var array
	 */
	private $piv = array();
	
	/**
	 *    LU Decomposition constructor.
	 *
	 * @param $A Rectangular matrix
	 * @return Structure to access L, U and piv.
	 */
	public function __construct($A)
	{
		if ($A instanceof PHPExcel_Shared_JAMA_Matrix) {
			// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
			$this->LU = $A->getArray();
			$this->m = $A->getRowDimension();
			$this->n = $A->getColumnDimension();
			for ($i = 0; $i < $this->m; ++$i) {
				$this->piv[ $i ] = $i;
			}
			$this->pivsign = 1;
			$LUrowi = $LUcolj = array();
			
			// Outer loop.
			for ($j = 0; $j < $this->n; ++$j) {
				// Make a copy of the j-th column to localize references.
				for ($i = 0; $i < $this->m; ++$i) {
					$LUcolj[ $i ] = &$this->LU[ $i ][ $j ];
				}
				// Apply previous transformations.
				for ($i = 0; $i < $this->m; ++$i) {
					$LUrowi = $this->LU[ $i ];
					// Most of the time is spent in the following dot product.
					$kmax = min($i, $j);
					$s = 0.0;
					for ($k = 0; $k < $kmax; ++$k) {
						$s += $LUrowi[ $k ] * $LUcolj[ $k ];
					}
					$LUrowi[ $j ] = $LUcolj[ $i ] -= $s;
				}
				// Find pivot and exchange if necessary.
				$p = $j;
				for ($i = $j + 1; $i < $this->m; ++$i) {
					if (abs($LUcolj[ $i ]) > abs($LUcolj[ $p ])) {
						$p = $i;
					}
				}
				if ($p != $j) {
					for ($k = 0; $k < $this->n; ++$k) {
						$t = $this->LU[ $p ][ $k ];
						$this->LU[ $p ][ $k ] = $this->LU[ $j ][ $k ];
						$this->LU[ $j ][ $k ] = $t;
					}
					$k = $this->piv[ $p ];
					$this->piv[ $p ] = $this->piv[ $j ];
					$this->piv[ $j ] = $k;
					$this->pivsign = $this->pivsign * -1;
				}
				// Compute multipliers.
				if (($j < $this->m) && ($this->LU[ $j ][ $j ] != 0.0)) {
					for ($i = $j + 1; $i < $this->m; ++$i) {
						$this->LU[ $i ][ $j ] /= $this->LU[ $j ][ $j ];
					}
				}
			}
		} else {
			throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::ARGUMENT_TYPE_EXCEPTION);
		}
	}
	
	/**
	 *    Get lower triangular factor.
	 *
	 * @return array Lower triangular factor
	 */
	public function getL()
	{
		for ($i = 0; $i < $this->m; ++$i) {
			for ($j = 0; $j < $this->n; ++$j) {
				if ($i > $j) {
					$L[ $i ][ $j ] = $this->LU[ $i ][ $j ];
				} elseif ($i == $j) {
					$L[ $i ][ $j ] = 1.0;
				} else {
					$L[ $i ][ $j ] = 0.0;
				}
			}
		}
		return new PHPExcel_Shared_JAMA_Matrix($L);
	}
	
	/**
	 *    Get upper triangular factor.
	 *
	 * @return array Upper triangular factor
	 */
	public function getU()
	{
		for ($i = 0; $i < $this->n; ++$i) {
			for ($j = 0; $j < $this->n; ++$j) {
				if ($i <= $j) {
					$U[ $i ][ $j ] = $this->LU[ $i ][ $j ];
				} else {
					$U[ $i ][ $j ] = 0.0;
				}
			}
		}
		return new PHPExcel_Shared_JAMA_Matrix($U);
	}
	
	/**
	 *    Return pivot permutation vector.
	 *
	 * @return array Pivot vector
	 */
	public function getPivot()
	{
		return $this->piv;
	}
	
	/**
	 *    Alias for getPivot
	 *
	 * @see getPivot
	 */
	public function getDoublePivot()
	{
		return $this->getPivot();
	}
	
	/**
	 *    Is the matrix nonsingular?
	 *
	 * @return true if U, and hence A, is nonsingular.
	 */
	public function isNonsingular()
	{
		for ($j = 0; $j < $this->n; ++$j) {
			if ($this->LU[ $j ][ $j ] == 0) {
				return false;
			}
		}
		return true;
	}
	
	/**
	 *    Count determinants
	 *
	 * @return array d matrix deterninat
	 */
	public function det()
	{
		if ($this->m == $this->n) {
			$d = $this->pivsign;
			for ($j = 0; $j < $this->n; ++$j) {
				$d *= $this->LU[ $j ][ $j ];
			}
			return $d;
		} else {
			throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::MATRIX_DIMENSION_EXCEPTION);
		}
	}
	
	/**
	 *    Solve A*X = B
	 *
	 * @param  $B  A Matrix with as many rows as A and any number of columns.
	 * @return  X so that L*U*X = B(piv,:)
	 * @PHPExcel_Calculation_Exception  IllegalArgumentException Matrix row dimensions must agree.
	 * @PHPExcel_Calculation_Exception  RuntimeException  Matrix is singular.
	 */
	public function solve($B)
	{
		if ($B->getRowDimension() == $this->m) {
			if ($this->isNonsingular()) {
				// Copy right hand side with pivoting
				$nx = $B->getColumnDimension();
				$X = $B->getMatrix($this->piv, 0, $nx - 1);
				// Solve L*Y = B(piv,:)
				for ($k = 0; $k < $this->n; ++$k) {
					for ($i = $k + 1; $i < $this->n; ++$i) {
						for ($j = 0; $j < $nx; ++$j) {
							$X->A[ $i ][ $j ] -= $X->A[ $k ][ $j ] * $this->LU[ $i ][ $k ];
						}
					}
				}
				// Solve U*X = Y;
				for ($k = $this->n - 1; $k >= 0; --$k) {
					for ($j = 0; $j < $nx; ++$j) {
						$X->A[ $k ][ $j ] /= $this->LU[ $k ][ $k ];
					}
					for ($i = 0; $i < $k; ++$i) {
						for ($j = 0; $j < $nx; ++$j) {
							$X->A[ $i ][ $j ] -= $X->A[ $k ][ $j ] * $this->LU[ $i ][ $k ];
						}
					}
				}
				return $X;
			} else {
				throw new PHPExcel_Calculation_Exception(self::MATRIX_SINGULAR_EXCEPTION);
			}
		} else {
			throw new PHPExcel_Calculation_Exception(self::MATRIX_SQUARE_EXCEPTION);
		}
	}
}